Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 408 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.The mean of 8 numbers is 16. When the number 7 is added to them, what is the new mean? (a) 14 (b) 17 (c) 15 (d) 16
2. 2.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 32 (b) 11 (c) 56 (d) 28
3. 3.A bag has 7 yellow, 5 red and 2 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 13/14 (b) 1/7 (c) 1/3 (d) 6/7
4. 4.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 264 (b) 51 (c) 240 (d) 480
5. 5.What is the mode of 17, 11, 1, 19, 17, 1 and 1? (a) 19 (b) 17 (c) 11 (d) 1
6. 6.What are the roots of x² − 7x + 12 = 0? (a) 1 and 6 (b) 2 and 6 (c) 3 and 4 (d) 1 and 12
7. 7.What is the midpoint of the line joining (1, 9) and (11, 11)? (a) (6, 10) (b) (12, 20) (c) (10, 6) (d) (5, 1)
8. 8.What are the roots of x² − 15x + 54 = 0? (a) 1 and 54 (b) 6 and 9 (c) 1 and 14 (d) 2 and 27
9. 9.A drawer has lots of white, green, black and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 8 (c) 5 (d) 4
10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 12 (d) 24
11. 11.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2504 (b) 2304 (c) 2704 (d) 2714
12. 12.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
13. 13.A cuboid is 10 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 360 sq cm (b) 166 sq cm (c) 664 sq cm (d) 332 sq cm
14. 14.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 553 (c) 543 (d) 552
15. 15.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 153 (c) 17 (d) 54
16. 16.A bag has 12 black balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 13 (b) 2 (c) 18 (d) 14
17. 17.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 45° (b) 135° (c) 125° (d) 100°
18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
19. 19.What is the mean of 2, 6, 8, 20, 4 and 14? (a) 8 (b) 11 (c) 10 (d) 9
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
21. 21.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 85° (c) 86° (d) 170°
22. 22.If a + b = 4 and ab = 3, what is (a − b)²? (a) 4 (b) 16 (c) 2 (d) 10
23. 23.What is the distance between the points (2, 24) and (14, 8)? (a) 400 (b) 20 (c) 28 (d) 21
24. 24.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 120 (d) 240
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/11 (c) 1/9 (d) 3/11
26. 26.If a + b = 13 and ab = 40, what is (a − b)²? (a) 169 (b) 89 (c) 9 (d) 3
27. 27.What is the median of 8, 22, 39, 10, 11, 17 and 34? (a) 22 (b) 10 (c) 17 (d) 11
28. 28.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 270 (b) 39 (c) 288 (d) 540
29. 29.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 55° (c) 125° (d) 70°
30. 30.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
31. 31.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 54 (c) 18 (d) 162
32. 32.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
33. 33.What is the midpoint of the line joining (2, 6) and (6, 2)? (a) (2, 2) (b) (5, 4) (c) (8, 8) (d) (4, 4)
34. 34.A drawer has lots of red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 4 (c) 3 (d) 2
35. 35.What is the 20th term of the AP 7, 15, 23, 31, …? (a) 167 (b) 160 (c) 159 (d) 152
36. 36.A bag has 4 blue, 6 red and 7 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 6/17 (b) 1/3 (c) 11/17 (d) 12/17
37. 37.What is the smallest prime factor of 133? (a) 19 (b) 7 (c) 1 (d) 2
38. 38.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 40°
39. 39.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 64 sq cm (d) 256 sq cm
40. 40.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 387 (d) 336

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